m25,q1

Question

Can anybody help me with this question?

Is  |x - 6| > 5 ?

1.  x  is an integer
 2.  x^2 < 1

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient

Bunuel · Answer

Let's work on the stem first. For which values of x, |x - 6| > 5 is true? |x - 6| > 5 x<6 --> -x+6>5 --> x<1. x>=6 --> x-6>5 --> x>11. So for x from the ranges x<1 and x>11 the inequality |x - 6| > 5 holds true. (1) x is an integer, clearly not sufficient. x can be 12 and the inequality holds true as we concluded OR x can be 5 and inequality doesn't hold true. (2) x^2<1 --> -1 5 holds true. Sufficient. Answer: B.

Tati · Answer

but in this case statement A contradicts to statement B. A states that x is an integer and B states that it is not.

Bunuel · Answer

Not so, taken together x can be zero which is an integer.

leochanGmat · Answer

If we need to indicate that x is an integer, shouldn't the answer be C?

Statement 1 alone: Insufficient. 
Statement 2 alone: 
-1<x<1 
|-1-6| = 7. True. 
However. 
|1-6| = 5. False 5 is not larger than 5. Also insufficient.

Both statement together: 
If say we take zero as an integer we need statement 1 to indicate that x is in fact an integer.

|0-6| = 6. True

Sufficient.

Bunuel · Answer

No, when considering the second statement we don't need to know that x is an integer. The question asks: "is x<1 or x>11?" and (2) says that -1<x<1, so we can answer YES to the question. In your examples you can not consider x=-1 and x=1 since in the given range (-1<x<1) -1 and 1 are not inclusive.

Hope it's clear.

leochanGmat · Answer

Thank you for the clarification.

Say if statement 2 is larger than 11, but not smaller than 1. The statement will still be sufficient?

m25,q1

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards